/usr/share/axiom-20170501/src/algebra/UPXS.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 | )abbrev domain UPXS UnivariatePuiseuxSeries
++ Author: Clifton J. Williamson
++ Date Created: 28 January 1990
++ Date Last Updated: 21 September 1993
++ Description:
++ Dense Puiseux series in one variable
UnivariatePuiseuxSeries(Coef,var,cen) : SIG == CODE where
Coef : Ring
var : Symbol
cen : Coef
I ==> Integer
L ==> List
NNI ==> NonNegativeInteger
OUT ==> OutputForm
RN ==> Fraction Integer
ST ==> Stream Coef
UTS ==> UnivariateTaylorSeries(Coef,var,cen)
ULS ==> UnivariateLaurentSeries(Coef,var,cen)
SIG ==> Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS),_
RetractableTo UTS) with
coerce : Variable(var) -> %
++ coerce(var) converts the series variable \spad{var} into a
++ Puiseux series.
differentiate : (%,Variable(var)) -> %
++ \spad{differentiate(f(x),x)} returns the derivative of
++ \spad{f(x)} with respect to \spad{x}.
if Coef has Algebra Fraction Integer then
integrate : (%,Variable(var)) -> %
++ \spad{integrate(f(x))} returns an anti-derivative of the power
++ series \spad{f(x)} with constant coefficient 0.
++ We may integrate a series when we can divide coefficients
++ by integers.
CODE ==> UnivariatePuiseuxSeriesConstructor(Coef,ULS) add
Rep := Record(expon:RN,lSeries:ULS)
getExpon: % -> RN
getExpon pxs == pxs.expon
variable upxs == var
center upxs == cen
coerce(uts:UTS) == uts :: ULS :: %
retractIfCan(upxs:%):Union(UTS,"failed") ==
(ulsIfCan := retractIfCan(upxs)@Union(ULS,"failed")) case "failed" =>
"failed"
retractIfCan(ulsIfCan :: ULS)
coerce(v:Variable(var)) ==
zero? cen => monomial(1,1)
monomial(1,1) + monomial(cen,0)
if Coef has "*": (Fraction Integer, Coef) -> Coef then
differentiate(upxs:%,v:Variable(var)) == differentiate upxs
if Coef has Algebra Fraction Integer then
integrate(upxs:%,v:Variable(var)) == integrate upxs
if Coef has coerce: Symbol -> Coef then
if Coef has "**": (Coef,RN) -> Coef then
roundDown: RN -> I
roundDown rn ==
-- returns the largest integer <= rn
(den := denom rn) = 1 => numer rn
n := (num := numer rn) quo den
positive?(num) => n
n - 1
stToCoef: (ST,Coef,NNI,NNI) -> Coef
stToCoef(st,term,n,n0) ==
(n > n0) or (empty? st) => 0
frst(st) * term ** n + stToCoef(rst st,term,n + 1,n0)
approximateLaurent: (ULS,Coef,I) -> Coef
approximateLaurent(x,term,n) ==
(m := n - (e := degree x)) < 0 => 0
app := stToCoef(coefficients taylorRep x,term,0,m :: NNI)
zero? e => app
app * term ** (e :: RN)
approximate(x,r) ==
e := rationalPower(x)
term := ((variable(x) :: Coef) - center(x)) ** e
approximateLaurent(laurentRep x,term,roundDown(r / e))
termOutput:(RN,Coef,OUT) -> OUT
termOutput(k,c,vv) ==
-- creates a term c * vv ** k
k = 0 => c :: OUT
mon :=
k = 1 => vv
vv ** (k :: OUT)
c = 1 => mon
c = -1 => -mon
(c :: OUT) * mon
-- check a global Lisp variable
showAll?:() -> Boolean
showAll?() == true
termsToOutputForm:(RN,RN,ST,OUT) -> OUT
termsToOutputForm(m,rat,uu,xxx) ==
l : L OUT := empty()
empty? uu => 0 :: OUT
n : NNI; count : NNI := _$streamCount$Lisp
for n in 0..count while not empty? uu repeat
if frst(uu) ^= 0 then
l := concat(termOutput((n :: I) * rat + m,frst uu,xxx),l)
uu := rst uu
if showAll?() then
for n in (count + 1).. while explicitEntries? uu and _
not eq?(uu,rst uu) repeat
if frst(uu) ^= 0 then
l := concat(termOutput((n :: I) * rat + m,frst uu,xxx),l)
uu := rst uu
l :=
explicitlyEmpty? uu => l
eq?(uu,rst uu) and frst uu = 0 => l
concat(prefix("O" :: OUT,[xxx ** (((n::I) * rat + m) :: OUT)]),l)
empty? l => 0 :: OUT
reduce("+",reverse_! l)
coerce(upxs:%):OUT ==
rat := getExpon upxs; uls := laurentRep upxs
count : I := _$streamCount$Lisp
uls := removeZeroes(_$streamCount$Lisp,uls)
m : RN := (degree uls) * rat
p := coefficients taylorRep uls
xxx :=
zero? cen => var :: OUT
paren(var :: OUT - cen :: OUT)
termsToOutputForm(m,rat,p,xxx)
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